Sure, you can hook up a low power serial transmitter to a Raspberry Pi's UART and have a text only console to operate over. But you are pretty much limited to text only and very slow file transer over a serial transmission like Kermit or Xmodem. You'll hate it for the type of computing you're used to. If you want a graphical remote desktop you are better off setting up a WiFi router/WLAN and connecting through a remote desktop connection. This will consume much more battery life, but I power a WiFi router with an RC LiPo battery and a voltage regulator and it lasts for several hours (but you certainly aren't getting days of battery life).
